Consider a reaction that is first order in both directions: $A \underset{K_b}{\stackrel{K_f}{\rightleftharpoons}} B$. Initially only $A$ is present,and its concentration is $A_{0}$. Assume $A_{t}$ and $A_{\text{eq}}$ are the concentrations of $A$ at time $t$ and at equilibrium,respectively. The time $t$ at which $A_{t} = (A_{0} + A_{\text{eq}})/2$ is $....$

$A$ reaction mixture containing $H_2, N_2$ and $NH_3$ has partial pressures of $2 \ atm, 1 \ atm$ and $3 \ atm$ respectively at $725 \ K.$ If the value of $K_P$ for the reaction,$N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ is $4.28 \times 10^{-5} \ atm^{-2}$ at $725 \ K,$ in which direction will the net reaction proceed?

At $473 \ K$, equilibrium constant $K_{c}$ for decomposition of phosphorus pentachloride, $PCl_{5}$, is $8.3 \times 10^{-3}$. If decomposition is depicted as,
$PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}, \Delta_{r}H^{\Theta} = 124.0 \ kJ \ mol^{-1}$
$(a)$ Write an expression for $K_{c}$ for the reaction.
$(b)$ What is the value of $K_{c}$ for the reverse reaction at the same temperature?
$(c)$ What would be the effect on $K_{c}$ if $(i)$ more $PCl_{5}$ is added $(ii)$ pressure is increased $(iii)$ the temperature is increased?

Which of the following is true for the reaction $H_2O_{(l)} \rightleftharpoons H_2O_{(g)}$ at $100 \ ^\circ C$ and $1 \ \text{atm}$ pressure?

Match List-$I$ (Equations) with List-$II$ (Type of processes) and select the correct option.

List-$I$ (Equations)	List-$II$ (Type of processes)
$A. K_p > Q$	$(i)$ Non-spontaneous
$B. \Delta G^\circ < RT \ln Q$	$(ii)$ Equilibrium
$C. K_p = Q$	$(iii)$ Spontaneous and endothermic
$D. T > \frac{\Delta H}{\Delta S}$	$(iv)$ Spontaneous

The values of $K_{P_1}$ and $K_{P_2}$ for the reactions
$X \rightleftharpoons Y + Z$ --- $(1)$
$A \rightleftharpoons 2B$ --- $(2)$
are in the ratio of $9 : 1$. If the degree of dissociation of $X$ and $A$ is equal,then the total pressure at equilibrium for $(1)$ and $(2)$ are in the ratio: